AWM-SIAM Sonia Kovalevsky Lecture Gets Auspicious Start in Montreal

October 31, 2003

Linda Petzold, the first AWM-SIAM Sonia Kovalevsky Lecturer, gave the audience a glimpse of her work on multiscale methods for chemically reacting systems, along with highlights of Kovalevsky's obstacle-laden route to her achievements in mathematics.

A speaker scheduled for the last afternoon of a meeting needs an intriguing topic, or at least plenty of enthusiasm for the work to be described. Linda Petzold of the University of California, Santa Barbara, brought both to the Friday-afternoon talk she gave at the SIAM Annual Meeting in Montreal. Titled "Towards the Multiscale Simulation of Bio-chemical Networks," the talk was the first AWM-SIAM Sonia Kovalevsky Lecture.

The Association for Women in Mathematics and SIAM established the lecture last year "to highlight significant contributions of women to applied or computational mathematics." Petzold, "in recognition of her fundamental contributions in the 1980s to the then-emerging field of differential-algebraic equations," had the honor of giving the first Kovalevsky Lecture. The citation goes on to credit her with "a significant impact in numerous areas of applied mathematics and computational science, resulting in two books and over 100 publications." Petzold is chair of the Computer Science Department and a professor in the Department of Mechanical and Environmental Engineering at UCSB, where she is also director of the Computational Science and Engineering program.

Those in the audience who were expecting to hear about differential-algebraic equations (for which Petzold also received SIAM's Germund Dahlquist Prize, in 1999) would have been surprised by her Kovalevsky Lecture. In it, Petzold described a project in which she's been involved for just over a year, working with postdoc Yang Cao at UCSB, former postdoc Muruhan Rathinam, now at the University of Maryland Baltimore County, and Daniel T. Gillespie of Dan T. Gillespie Consulting, on a multiscale computational framework for chemically reacting systems.

Multiscale numerical methods are needed for the simulation of microscopic systems formed by living cells, Petzold and colleagues point out in a forthcoming paper.* Existing schemes, they explain, are inefficient because of the multiscale nature of the underlying problem---a consequence of both the stiffness of the problem---the presence of multiple timescales---and the need to include in the simulation both species that are present in small quantities (which should be modeled by discrete stochastic processes), and species present in larger quantities (which can be modeled more efficiently by deterministic differential equations).

Focusing on the problem of stiffness in discrete stochastic systems, Petzold and her colleagues have developed stable methods based on the lyrically named "tau-leaping" methods recently proposed by Gillespie (and notable in being able to take timesteps that encompass more than one reaction). Specifically, they have proposed implicit tau-leaping methods that, they believe, can overcome some of the limitations of Gillespie's explicit methods. In Montreal, Petzold briefly outlined the current status of analytical and numerical results in this area.Clearly pleased with the results to date and happy to have the opportunity to present this work-in-progress to a receptive audience, Petzold nonetheless graciously carved a few minutes out of her talk for a tribute to the late-19th-century Russian mathematician for whom the lecture is named.Highlights of the information she presented to the audience in Montreal, gleaned from reading she did on learning of the AWM-SIAM award, can be found in the sidebar.

In concluding her tribute, Petzold pointed to the many barriers that Kovalevsky had to overcome in the course of her career. Women in science today still encounter obstacles, she said; although less onerous than those facing Kovalevsky, they remain considerable. Further information can be found in the report "A Study on the Status of Women Faculty in Science at MIT" (MIT, 1999).

The Remarkable Career of Sonia KovalevskyThe most well known Russian mathematician of her time, Sonia Kovalevsky (who also wrote novels, poetry, and theatre reviews) was the first woman to receive a doctorate in mathematics (1874, summa cum laude, from the University of Göttingen). This path-making achievement, all the more impressive in light of the obstacles that Kovalevsky had to overcome in pursuing it, was based on three remarkable research papers, each deemed worthy of a doctorate by Weierstrass, with whom Kovalevsky worked in Berlin (without, as a woman, being allowed to take courses at the university); the papers were on partial differential equations, Abelian integrals, and the rings of Saturn.

Despite the support of her prestigious mentor, the best Kovalevsky could do job-wise was a position teaching arithmetic to elementary school girls. The later intercession of another influential mentor---Mittag-Leffler---led in 1889 to a move to another country and to an appointment at the University of Stockholm, where she was one of the first women to hold a chair in a European university. It was in Stockholm that she did what some consider her most important work. In 1888, she received the Prix Bordin of the French Academy of Sciences (given in recognition of outstanding results in the study of a rigid body); Kovalevsky's paper was titled "Mémoire sur un cas particulier du problème de la rotation d'un corps pesant autour d'un point fixe, où l'intégration s'effectue à l'aide des fonctions ultra-elliptiques du temps." The academy, signaling its appreciation for the brilliance of the work, increased the prize from 3000 to 5000 francs.

In Stockholm, in addition to her research, Kovalevsky taught courses in analysis. During that time she also became an editor of the then new Acta Mathematica, in addition to serving as a liaison with mathematicians in Paris and Berlin and playing an active role in the organization of international conferences.

By the end of her life, she had been elected to the Russian Academy of Sciences, although her hopes of an offer of a position at a Russian university were never realized. Kovalevsky died in Stockholm in 1891.